BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-72-278
       ENTRY:: October 16, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: Use of fast direct methods for the efficient numerical
               solution of nonseparable elliptic equations.
        TYPE:: Technical Report
      AUTHOR:: Concus, Paul
      AUTHOR:: Golub, Gene H.
        DATE:: April 1972
       PAGES:: 41
    ABSTRACT:: We study an iterative technique for the numerical solution of
               strongly elliptic equations of divergence form in two
               dimensions with Dirichlet boundary conditions on a rectangle.
               The technique is based on the repeated solution by a fast
               direct method of a discrete Helmholtz equation on a uniform
               rectangular mesh. The problem is suitably scaled before
               iteration, and Chebyshev acceleration is applied to improve
               convergence. We show that convergence can be exceedingly
               rapid and independent of mesh size for smooth coefficients.
               Extensions to other boundary conditions, other equations, and
               irregular mesh spacings are discussed, and the performance of
               the technique is illustrated with numerical examples.
       NOTES:: [Adminitrivia V1/Prg/19951016]
         END:: STAN//CS-TR-72-278